Quasi-circles and Maximal Surfaces in the Pseudo-hyperbolic Space

par Prof. Jérémy Toulisse (Université de Nice-Sophia Antipolis)

lundi 7 oct. 2019, 16:30 → 17:45 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Quasi-circles in the complex plane are fundamental objects in complex analysis; they were used by Bers to define an infinite-dimensional analogue of the usual Teichmüller space. After introducing the notion of quasi-circles in the boundary of the pseudo-hyperbolic space $H^{2,n}$, I will explain how to construct a unique complete maximal surface in $H^{2,n}$ bounded by a given quasi-circle. This construction relies on Gromov's theory of pseudo-holomorphic curves and provides a generalization of maximal representations of surface groups into rank 2 Lie groups. This joint work with François Labourie and Mike Wolf.